Simulating Complex Satellites and a Space-Based ... · PDF fileSimulating Complex Satellites and a Space-Based Surveillance Sensor Simulation Cody R. Singletary and Francis K. Chun

Simulating Complex Satellites and a Space-Based Surveillance Sensor Simulation

Cody R. Singletary and Francis K. Chun Department of Physics, U.S. Air Force Academy

ABSTRACT

Maintaining space situational awareness requires the ability to track earth-bound satellites in order to know and predict their position, movement, size, and physical features. However, there are many satellites in orbit that are simply too small or too far away to resolve by conventional optical imaging. We can use photometric techniques to gather information about the body in question, but the problem comes in how we interpret the light curve data. Light curves are created by measuring the intensity of reflected sunlight off of the object as it passes overhead. The intensity is dependent on a variety of factors to include the size, shape, orientation, and material composition of the satellite. When we attempt to solve the inverse problem for light curves, we are attempting to extract information about these different factors. Forward modeling of photometric light curves provides a way to generate a large amount of data under controlled conditions for working the inverse problem and is an effective way to test Non-Resolved Space Object Identification (NRSOI) techniques. Currently, there are few implementations of such modeling programs, one of which only allows simple geometric shapes with the option of antennas. We present our modification to that existing code to create complex models plus our new code to calculate shadowing on the complex object. Then we show the results from the new model and a comparison to the original tool. The next generation of space surveillance sensors will be on satellites. Space based sensors avoid many of the problems of ground based sensors, such as, waiting for lighting conditions to match satellite passes and a night sky. These sensors are restricted only by sun exclusion angle and line of sight around the Earth. This allows for more effective techniques and a much longer time on target. We present an addition to the existing code to consider a sensor in orbit. The code is generalized to provide flexibility in testing different orbital parameters and provides pass prediction with predictive forward modeling for any orbit.

1. INTRODUCTION

Space situational awareness is a mission of growing importance for the Air Force and the United States. As more and more countries develop their space capabilities, it will become vital for the U.S. to maintain awareness of all objects orbiting the earth, especially as it pertains to U.S. security and space capability. Being able to track satellites in order to maintain a catalog, will need to evolve into characterizing those satellites. High-resolution imagery of satellites will certainly provide a means of characterization, but as satellites become smaller or as the range to satellites increases, it will become harder and harder to obtain the requisite high-resolution imagery (Fig. 1). Thus other means for characterizing satellites will need to be developed. Research into non-resolvable space object identification techniques is beginning, especially with the adaptation of standard astronomical observational techniques to satellites. Analysis of a satellite’s time-varying photometric signature can provide some information on its form, fit, and function.

A satellite’s photometric light curve is the intensity of reflected sunlight off of the object as it passes overhead. The intensity is dependent on a variety of factors to include the size, shape, orientation, and material composition of the satellite. When we attempt to invert a satellite’s light curve, we are attempting to extract information about these different factors.

Forward modeling of photometric light curves provides a way to generate a large amount of data under controlled conditions for working the inverse problem and is an effective way to test Non-Resolved Space Object Identification (NRSOI) techniques. Currently there are two ways of generating this data. One is to use ray-tracing on a complex model of the satellite, a task which requires enormous computing power and time. The second way, which we are using here is to create simpler models of satellite bodies and use albedo-area calculations with the Cook-Torrance BRDF model. This is a much faster, albeit less accurate method.

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4. TITLE AND SUBTITLE Simulating Complex Satellites and a Space-Based Surveillance Sensor Simulation

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13. SUPPLEMENTARY NOTES 2009 Advanced Maui Optical and Space Surveillance Technologies Conference, 1-4 Sep, Maui, HI.

14. ABSTRACT Maintaining space situational awareness requires the ability to track earth-bound satellites in order toknow and predict their position, movement, size, and physical features. However, there are many satellitesin orbit that are simply too small or too far away to resolve by conventional optical imaging. We can usephotometric techniques to gather information about the body in question, but the problem comes in howwe interpret the light curve data. Light curves are created by measuring the intensity of reflected sunlightoff of the object as it passes overhead. The intensity is dependent on a variety of factors to include the size,shape, orientation, and material composition of the satellite. When we attempt to solve the inverse problemfor light curves, we are attempting to extract information about these different factors. Forward modelingof photometric light curves provides a way to generate a large amount of data under controlled conditionsfor working the inverse problem and is an effective way to test Non- Resolved Space Object Identification(NRSOI) techniques. Currently, there are few implementations of such modeling programs, one of whichonly allows simple geometric shapes with the option of antennas. We present our modification to thatexisting code to create complex models plus our new code to calculate shadowing on the complex object.Then we show the results from the new model and a comparison to the original tool. The next generation ofspace surveillance sensors will be on satellites. Space based sensors avoid many of the problems of groundbased sensors, such as, waiting for lighting conditions to match satellite passes and a night sky. Thesesensors are restricted only by sun exclusion angle and line of sight around the Earth. This allows for moreeffective techniques and a much longer time on target. We present an addition to the existing code toconsider a sensor in orbit. The code is generalized to provide flexibility in testing different orbitalparameters and provides pass prediction with predictive forward modeling for any orbit.

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a. REPORT unclassified

b. ABSTRACT unclassified

c. THIS PAGE unclassified

Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18

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Fig. 3. Engagement #1. The top panel shows the simulated results of the photometric tool. The image of the globe includes the terminator, a sensor site indicated by the red plus sign, and the satellite pass in yellow moving from north to south. The complex body image is the orientation of the satellite as seen from the sensor site. The plot of intensity (I) versus time shows the overall intensity in white and individual facet intensities in blue. Finally, the bottom panel is a plot of residuals or difference between the complex body with shadowing and the complex body without shadowing.

The second pass (Fig. 4, Engagement #2) we present is for the complex body in an orbit associated with SSN Object 28773 (560 km altitude, 31.41º inclination, RAAN of 335.71º, and eccentricity of 0.0007). On February 5, 2007, there is a dusk pass observed from AEOS between 0430-0500 UT which crosses the terminator at a 90° angle. This satellite was also given an axial spinner attitude. Initially, the satellite begins the pass oriented with its spin axis toward the observer. The residuals in the first third of the light curve have a higher frequency than the actual rotation rate of the satellite, however the last two-thirds of the residual plot shows shadowing occurring at the rotation frequency of the satellite. Further analysis is required to understand the difference in the shadowing frequency.

Fig. 4. Engagement #2. Same format as Fig. 3.

The final pass (Fig. 5, Engagement #3) we present is for the complex body in an orbit associated with SSN Object 27844 (1171 km altitude, 42.2º inclination, RAAN of 83.55º, and eccentricity of 0.0011). On March 13, 2009, there was a dawn pass observed at AEOS between 1545-1558 UT which crosses the terminator at a 45° angle. Contrary to the previous cases, this satellite was in a nadir-ram stabilized attitude with its body x-axis pointing to the ram and its body z-axis pointing to nadir. For this engagement, the satellite begins the pass oriented with its ram axis nearly toward the observer. As the satellite moves through its orbit, the observer begins to see an increasing and systematic shadowing effect as indicated in the residual plot. One does not see any periodic shadowing due to satellite spin since the satellite is not spinning. Additionally, as the satellite passes the observer and across the terminator, the “solar panel” appendages appear to reduce the overall intensity from the side facets of the main body as one would expect. 

Fig. 5. Engagement #3. Same format as Fig. 3.

We may draw three basic conclusions from this data shown above. First, the shadowing code appears to account for one facet shadowing another facet. Second, the shadowing effect appears consistent with the satellite attitude as seen by the marked differences in the residuals between the axial-spinner and nadir-ram pointing attitudes. Finally, we were able to “measure” the shadowing effect by comparing a complex body with shadowing to one without shadowing. However, when observing an actual satellite in orbit and measuring its time-varying photometric light curve, one must devise a way to determine whether the object is indeed a complex shape exhibiting shadowing, or a simple object with no shadowing.

3. SPACE-BASED SENSOR MODELING

3.1 Pass Prediction and Visualization

The photometric tool created by AFRL and modified as described above to accommodate complex shapes has one limitation. Currently, it can only model satellites as observed from fixed ground sites. Theoretically, this tool can model a sensor site at a fixed longitude and latitude, but at an altitude representative of a satellite orbit. Of course, in doing so, one does not even come close to modeling the effects of the sensor movement on the target’s photometric light curve. With future space-based sensors planned, we decided to modify the AFRL tool to model a satellite’s photometric light curve as measured by another orbiting satellite. Most of the tool’s functions and routines were still applicable, except that now we had to modify the code to accept orbit parameters for the sensor satellite and predict when the sensor satellite will be able to observe the target satellite under various constraints such as a sun-exclusion angle and no measurements against the hard earth background. The first step in the modification was to rewrite the pass prediction code. The current pass prediction algorithm takes two-line elements (TLEs) of the observing satellite and propagates them using SGP4. It then finds the TLEs of the target satellite and propagates it using the observing satellite’s coordinates as the “ground observer” coordinates. Once both orbits were propagated, we had to calculate all ephemeris points where the Earth and the sun

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The authorand their oPerformanDetachmenResearch PMr. Joe Ko

1. Hall D.

. Phase angle-hase angle is onent on the cu

ing, we noticedn pass. This isor would. Add

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o thank Dr. Donts, suggestionModernization

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4. CO

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5. ACKNO

oyle Hall and Mns, and recommn Program Offiboratory for th

of this researchorate, Air Forc

6. R

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ONCLUSION

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wing function, ades combining iailable coverag

OWLEDGEM

Mr. Paul Kervinmendations. Wfice, the Maui Hheir support to th was conductee Research Lab

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NS

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and creating a git with the shadge for different

MENTS

n for the use ofe also thank th

High Performanthe U.S. Air Fod. Finally, thisboratory.

S

esolved Object

er (right plot) frhe structure fro

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etric modeling of Defense Higg Center and Cadet Summefunded in part

AMOS Technic

es. ar

very d-ther, get is ed to

e gles known

ppear metric osite GUI. time-oping

tool gh

er t by

cal

Conference Proceedings, Kihei, HI, 2007.

2. Hall D., “Optical CubeSat Discrimination,” The 2008 AMOS Technical Conference Proceedings, Kihei, HI, 2008. 3. "Tetrahedron." Wikipedia, The Free Encyclopedia. 26 Aug 2009, 21:44 UTC. 26 Aug 2009 <http://en.wikipedia.org/w/index.php?title=Tetrahedron&oldid=310245038>.